Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T13:40:02.277Z Has data issue: false hasContentIssue false
  • English
  • Français

Combined Effects of EDL and Boundary Slip on the Stability of Liquid-Liquid Viscosity-Stratified Flow in Microchannels

Published online by Cambridge University Press:  18 May 2015

L.-D. Zhang  and
X.-Y. You
L.-D. Zhang
Affiliation:
School of Environmental Science and Engineering Tianjin University Tianjin, China
X.-Y. You*
Affiliation:
School of Environmental Science and Engineering Tianjin University Tianjin, China
*
* Corresponding author (xyyou@tju.edu.cn)
Get access

Abstract

The stability of pressure-driven liquid-liquid viscosity-stratified microchannel flow is investigated by considering the combined effects of electrical double layer (EDL) and boundary slip. The electrical streaming currents determined by the Streaming Electrical Current Balance (ECB) and the boundary slip are considered by Navier slip assumption. The stability of flow is studied by the small disturbance theory. Numerical results indicate that the effect of boundary slip on the flow stability is strongly depended on the EDL. The boundary slip stables the flow when EDL effect is weak and destabilizes the flow when EDL effect is strong. The effects of boundary slip and EDL on flow stability is also determined by viscosity ratio, the height of channel, interface position and conductivity ratio.

Keywords

Electrical double layer (EDL)Boundary slipMicrochannelStabilityLiquid-liquid viscosity-stratified flow
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 5 , October 2015 , pp. 597 - 606
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Tokeshi, M., Minagawa, T. and Kitamori, T., “Integration of a Microextraction System on a Glass Chip: Ion-Pair Solvent Extraction of Fe (II) with 4, 7-Diphenyl-1, 10-phenanthrolinedisulfonic Acid and Tri-n-octylmethylammonium Chloride,” Analytical Chemistry, 72, pp. 1711–1714 (2000).Google Scholar
2.Berthier, J., Tran, V. M., Mittler, F. and Sarrut, N., “The Physics of a Coflow Micro-Extractor: Interface Stability and Optimal Extraction Length,” Sensors and Actuators A: Physical, 149, pp. 56–64 (2009).Google Scholar
3.Hibara, A., Tokeshi, M., Uchiyama, K., Hisamoto, H. and Kitamori, T., “Integrated Multilayer Flow System on A Microchip,” Analytical Sciences, 17, pp. 89–93 (2001).CrossRefGoogle ScholarPubMed
4.Kuban, P., Berg, J. and Dasgupta, P. K., “Vertically Stratified Flows in Microchannels. Computational Simulations and Applicatons to Solvent Extraction and Ion Exchange,” Analytical Chemistry, 75, pp. 3549–3556 (2003).CrossRefGoogle Scholar
5.Yih, C.-S., “Instability Due to Viscosity Stratification,” Journal of Fluid Mechanics, 27, pp. 337–352 (1967).CrossRefGoogle Scholar
6.Charles, M. E. and Lilleleht, L. U., “An Experimental Investigation of Stability and Interfacial Waves in Co-Current Flow of Two Liquids,” Journal of Fluid Mechanics, 22, pp. 217–224 (1965).Google Scholar
7.Kao, T. W. and Park, C., “Experimental Investigations of the Stability of Channel Flows. Part 2 Two-Layered Co-Current Flow in a Rectangular Channel,” Journal of Fluid Mechanics, 52, pp. 401–423 (1972).Google Scholar
8.Yiantsios, S. G. and Higgins, B. G., “Linear Stability of Plane Poiseuille Flow of Two Superposed Fluids,” Physics of Fluids, 31, pp. 3225–3238 (1988).Google Scholar
9.Hooper, A. P., “The Stability of Two Superposed Viscous Fluids in a Channel,” Physics of Fluids, 1, pp. 1133–1142 (1989).CrossRefGoogle Scholar
10.Puccetti, G., Pulvirenti, B. and Morini, G. L., “Experimental Determination of the 2D Velocity Laminar Profile in Glass Microchannels using µPIV,” Energy Procedia, 45, pp. 538–547 (2014).Google Scholar
11.Yang, X. and Zheng, Z. C., “Effects of Channel Scale on Slip Length of Flow in Micro/Nanochannels,” Journal of Fluids Engineering, 132, p. 061201 (2010).CrossRefGoogle Scholar
12.Das, S. and Chakraborty, S., “Effect of Conductivity Variations Within the Electric Double Layer on the Streaming Potential Estimation in Narrow Fluidic Confinements,” Langmuir, 26, pp. 11589–11596 (2010).Google Scholar
13.You, X. Y., Zheng, X. J. and Zheng, J. R., “Molecular Theory of Liquid Apparent Viscosity in Micro-channels,” Acta Physica Sinica, 56, pp. 2323–2329 (2007) [in Chinese].Google Scholar
14.Lauga, E. and Cossu, C., “A Note on the Stability of Slip Channel Flows,” Physics of Fluids, 17, p. 088106 (2005).Google Scholar
15.You, X. Y., Zheng, J. R. and Jing, Q., “Effects of Boundary Slip and Apparent Viscosity on the Stability of Microchannel Flow,” Forsch Ingenieurwes, 71, pp. 99–106 (2007).Google Scholar
16.You, X. Y., Zhang, L. D. and Zheng, J. R., “The Stability of Finite Miscible Liquid-Liquid Stratified Microchannel Flow with Boundary Slip,” Journal of Mechanics, 30, pp. 103–111 (2013).Google Scholar
17.Tardu, S., “Interfacial Electrokinetic Effect on the Microchannel Flow Linear Stability,” Journal of Fluids Engineering, 126, pp. 10–13 (2004).CrossRefGoogle Scholar
18.Tardu, S., “The Electric Double Layer Effect on the Microchannel Flow Stability and Heat Transfer,” Superlattice Microstructures, 35, pp. 513–529 (2004).Google Scholar
19.You, X. Y. and Guo, L. X., “Combined Effects of EDL and Boundary Slip on Mean Flow and its Stability in Microchannels,” Comptes Rendus Mécanique, 338, pp. 181–190 (2010).CrossRefGoogle Scholar
20.Yang, J. and Kwok, D. Y., “Effect of Liquid Slip in Electrokinetic Parallel-Plate Microchannel Flow,” Journal of Colloid and Interface Science, 260, pp. 225–233 (2003).Google Scholar
21.Li, J., Sheeran, P. S. and Kleinstreuer, C., “Analysis of Multi-Layer Immiscible Fluid Flow in a Micro-channel,” Journal of Fluids Engineering, 133, p. 111202 (2011).Google Scholar
22.You, X. Y. and Zheng, J. R., “Stability of Liquid-Liquid Stratified Microchannel Flow under the Effects of Boundary Slip,” International Journal of Chemical Reactor Engineering, 7, p. A85 (2009).Google Scholar
23.Ozen, O., Aubry, N., Papageorgiou, D. T. and Petropoulos, P. G., “Electrohydrodynamic Linear Stability of Two Immiscible Fluids in Channel Flow,” Electrochimica Acta, 51, pp. 5316–5323 (2006).Google Scholar
24.Zhang, J., Zahn, J. D. and Lin, H., “A General Analysis for the Electrohydrodynamic Instability of Stratified Immiscible Fluids,” Journal of Fluid Mechanics, 681, pp. 293–310 (2011).Google Scholar
25.Park, H. M., “Zeta Potential and Slip Coefficient Measurements of Hydrophobic Polymer Surfaces Exploiting a Microchannel,” Industrial & Engineering Chemistry Research, 51, pp. 6731–6744 (2012).Google Scholar
26.You, X. Y., “Feedback Control of the Instability of a Fluid Layer Flowing Down a Vertical Cylinder,” International Journal of Heat and Mass Transfer, 45, pp. 4537–4542 (2002).Google Scholar
27.Mala, G. M. and Li, D. Q., “Flow Characteristics of Water Through a Microchannel Between Two Parallel Plates with Electrokinetic Effects,” International Journal of Heat and Fluid Flow, 18, pp. 489–496 (1997).Google Scholar
28.Hao, P. F., Zhang, X. W., Yao, Z. H. and He, F., “Transitional and Turbulent Flow in a Circular Microtube,” Experimental Thermal and Fluid Science, 32, pp. 423–431 (2007).CrossRefGoogle Scholar
29.Pohar, A., Lakner, M. and Plazl, I., “Parallel Flow of Immiscible Liquids in a Microreactor: Modeling and Experimental Study,” Microfluidics and Nanofluidics, 12, pp. 307–316 (2012).Google Scholar
30.Peng, X. F., Peterson, G. P. and Wang, B. X., “Heat-Transfer Characteristics of Water Flowing Through Microchannels,” Experimental Heat Transfer, 7, pp. 265–283 (1994).Google Scholar
31.Wang, B. X. and Peng, X. F., “Experimental Investigation on Liquid Forced-Convection Heat Transfer Through Microchannels,” International Journal of Heat and Mass Transfer, 37, pp. 73–82 (1994).Google Scholar